joigus

Because the theory predicts that charged particles with this angular momentum of spin will deflect in a magnetic field; and the deflection has been measured --Stern-Gerlach experiment. That was the epochal experiment that's still very much in use. There are others based on photon emission, etc. There are many, many other indirect checks. Ferromagnetism, for example.

Thank you, Zapatos. I've found a little bit more of the geological history on Wikipedia: https://en.wikipedia.org/wiki/Kegon_Falls From https://www.visitnikko.jp/en/spots/kegon-falls/ The place is such a tourist magnet that it's kinda difficult to find something more science-oriented about it: Geology, fauna and flora, etc.

Another real-estate agency's hopes have been shattered, as we speak.

I always thought they were laughing.

I think you're confusing what equation (problem) you actually have, and what values of \( k \) make sense for your problem. You also seem to have some confusion about what values of \( k \) are valid for your problem. In your OP, you're proposing up to four different equations: \[x^{2}+1-1/k=0\] \[x^{2}+1-1/k=1\] \[x^{2}+1+1/k=0\] \[x^{2}+1+1/k=1\] So the first question I would ask you is: Which one is it? Maybe you want to solve all of them. The question about what values of \( k \) make sense is simpler. Only those with \( k\neq0 \) make sense for the equations you've written. Moving something or other to the right hand side has nothing to do with it, unless you do it multiplicatively. For example, if your equation were, \[k\left(x^{2}-k\right)=1\] you would have to be careful not to divide by \( k \) in case that parameter were \( 0 \). In general, when you have both unknowns (the thing you want to solve for) and parameters (which define an infinite family of possible equations, one for each possible value of the parameter), you must discuss the equation for every possible value of the parameter. And you must leave out those values of the parameter that don't give a sensible equation. I hope that helps.

NASA has found water on the Moon's lit surface. https://www.npr.org/2020/10/26/927869069/water-on-the-moon-nasa-confirms-water-molecules-on-our-neighbors-sunny-surface?t=1603753199805 https://www.nature.com/articles/s41550-020-01222-x#_blank Abstract from Nature Astronomy: Interesting news, though not Earth-shattering, probably.

Thanks @Bufofrog and @Phi for All for noticing and acting accordingly. I was asking --rhetorically-- and Kartazion removed the question words so that the rhetoric was changed.

I also would like to know why it would be impossible to reveal to the general public.

Testing some inline maths like \( d^{3n}xd^{3n}p\rho\left(x,p\right) \), \( y = x^2 \) or \( \varepsilon_{\alpha\beta\gamma}\varepsilon_{\alpha\mu\nu}=\delta_{\beta\mu}\delta_{\gamma\nu}-\delta_{\beta\nu}\delta_{\gamma\mu} \) should work.

Nice anecdote. Thanks for sharing. As I said, I was really clumsy in the laboratory. But one thing I did well: I never crossed out any data reading because they gave a freak result. They all made it to my error bars. They were probably just fluctuations, some due to my sloppiness.

Are you implying that asking whether science can prove the existence of 17 balls of jello, each with the mind of a baby, but whose mutual communication results into a common mega intelligence that rules our universe is a ridiculous question?

You're welcome.

It's not a metaphor; it's an analogy. Do you know the difference?

No. It's, \[\gamma^{2}\left(1-\beta^{2}\right)=1\] Gamma is a number always bigger than one. Beta is a number always less than one (in absolute value.) The absolute value of beta determines gamma.

Maybe I missed something all those years of measuring with ammeters and voltimeters, and oscilloscopes. Differentiating the equations to get the error formulas, actually doing the experiment, crunching the numbers for the analysis of errors, and reporting the results. I cannot guess the pointless next step of your "idea" because it's impossible to guess what's going to come next after a babbling nonsense like yours. Last time I measured it in a laboratory of electricity, Faraday's law was correct to within the error bars. Even though I was a terrible experimentalist, not even I was able to get it wrong. And then studying the theory and learning how to solve the equations forwards and backwards... Faraday's law is actually necessary for the Lorentz symmetry of the theory. Angular momentum in particular would not be well defined or conserved either. The symmetries are too tight. You need it for charge conservation too. The homogeneous terms of the Maxwell equations are actually forced upon you from a pure geometric identity (Bianchi identity) or from first principles of mechanics, after you arrange the E and B fields in their proper Lorentz-invariant form (Feynman's proof of Maxwell's equations.) But first you must understand also what a gauge theory is, something you cannot even begin to fathom. Moronic pseudo-science. That's what your sorry excuse for an idea is. Sleep well.

You don't make any sense, how can I guess what you're going to say next? You are clueless about electromagnetism. That's all I can say. No matter how many colours you use in your drawings. As to the mathematics (no wonder it's absent in your explanation), I can't even begin to tell you how inconsistent your idea is with everything we know. And finally, what you're saying is falsified by experiments every which way.

Utter nonsense.

No. Computers "solve" equation by getting approximate solutions. Humans who want to solve non-linear equations must be clever. That's what I mean.

No. It's neither delicate nor embarrassing. It's a little bit like asking: Can science prove the existence of 17 balls of jello, each with the mind of a baby, but whose mutual communication results into a common mega intelligence that rules our universe? Split of Theory of everything It's just as delicate and as embarrassing IMO.

Not really. Not in general. You might get lucky and pull it off in particular examples. For example, consider the (non-linear) system: \[x^{2}-y^{2}=a\] \[x+y=b\] And assume, \[b\neq0\] The first equation is non-linear, because it involves powers of x and y different from 1. But you could use the second one to substitute x+y in, \[x^{2}-y^{2}=\left(x+y\right)\left(x-y\right)\] and get to the linear system, \[x-y=\frac{a}{b}\] \[x+y=b\] which can be solved by Gauss (by adding and subtracting both eqs.) to get, \[2x=b+\frac{a}{b}\] \[2y=b-\frac{a}{b}\] So that, \[x=\frac{b^{2}+a}{2b}\] \[y=\frac{b^{2}-a}{2b}\] That's the problem with non-linear equations. Each one is different.

Absolutely not. Gauss elimination is for linear equations; GR is highly non-linear. "Linear" means that a combination of solutions S1, S2, like 2S1 + S2, or -S1 + 3S2, etc., is also a solution. That is, linear combinations of solutions are also solutions. Also, the Gauss method is only valid for numeric equations, not for differential equations. GR is set in terms of differential equations (equations that involve the derivatives of an unknown function.) I hope that helped.

How come identical situation (orientation, angular velocity,...) of the magnets and the rotating circuit gives rise to opposite effects in I-II and in III-IV?

Yes. I've noticed that OP was using the term in a different sense. Very inspired and inspiring comment, by the way.

Mating-brilliant. (@ Koti.)

Just to take up on @studiot's suggestion. An idea that you may find silly, but has helped me a lot during hard times is the thought that clouds keep rolling over my head no matter what I think. A similar mindset you can find here: